OAVS TGT Math Mock Test - 1 - OTET MCQ

We have total cards = 52
4 categories=spades,clubs,diamonds and hearts
Spades and clubs are black cards
No. of favourable outcomes=13+13=26
Probability of getting a black card= no. of favourable outcomes/total no. of outcomes
=26/52=1/2

Area of the circle with radius r =πr²
Now, New Radius = r + 100% of r = r + r = 2r
∴ New Area = π(2r)² - 4πr²
∴ Increased Area = 4πr² -  πr² = 3πr²
And Area increased in

Let the angle be x. Its complement will be 90 - x. Therefore,

x = 90 - x 

=> 2x = 90 

=> x = 45 degree

The answer is 45 degree.

We have the numbers from 1 to 12. Total possible outcomes = 12 Now, divisors of 12 : 1, 2, 3, 4, 6 and 12 Number of divisors of 12 = 6 Number of favourable outcomes = 6 
Required probability 

Corresponding sides in congruent triangles are equal.

So AC = PR ,AB = PQ ,BC = QR

The point D(3, -6) lies in the IV Quadrant.
Explanation: In the Cartesian plane, the X-axis and Y-axis divide the plane into four quadrants. The I Quadrant is where both x and y are positive. The II Quadrant is where x is negative and y is positive. The III Quadrant is where both x and y are negative. The IV Quadrant is where x is positive and y is negative.
The point D(3, -6) has a positive x-coordinate and a negative y-coordinate. Therefore, it lies in the IV Quadrant.

We have the sequence 5n²+2n+3
It will be in AP if it satisfies an-an-1=d where d is a constant.
Here, a_n=5n²+2n+3
And, a_n-1=5(n-1)²+2(n-1)+3=5(n²+1-2n)+2n-2+3
=5n²+5-10n+2n+1=5n²-8n+6
a_n-a_n-1=5n²+2n+3-(5n²-8n+6)
=5n²+2n+3-5n²+8n-6
=10n-3, which depends on a variable , so its not constant.

(1). If a triangle has all the angles greater than 60∘, the sum of angles of the triangle will be more than 180∘
Only (2). is correct because if all the angles are equal, triangle will be an equilateral triangle and sum of all the angles of the triangle will be 180∘.

When b² - 4ac=0 then we have the root as -b/2a.
When  b²-4ac < 0,then the root is a complex root ,since we have a negative number ,for which real square root is not possible.
When b² - 4ac > 0 then we have a square root of it and hence we have real roots. So the correct answer is b² - 4ac > 0

Two coins are simultaneously tossed.
So sample space={HH,HT,TH,TT}
No. of favourable outcomes=getting at least one head={HH,HT,TH}
=3
Total number of outcomes=4
Probability of getting at least one head=No. of favourable outcomes/Total number of outcomes
=3/4

LCM (12, 15, 18, 27) = 540
Now, largest four digit number = 9999 
∴ 9999 ÷ 540 = 18 x 540 + 279 (Remainder = 279) Therefore, the largest number of 4 digits exactly divisible by 12, 15, 18 and 27 is 9999 – 279 = 9720

Therefore, the length of the shadow is 10m long.

we have, 

2 = (3p - 2)/2   and 2p + 2  = (2q + 4)/2

3p = 6  and 2p = q

p = 2

and q = 2p = 4

sin 45° + cos 45°

Hence, the answer is = √2

Then, a_{n – 1} = 3(n – 1)² – 4(n – 1)

= 3n² + 3 – 6n – 4n + 4 = 3n² – 10n + 7

a_n = S_n – S_{n – 1}

a_n = 3n² – 4n – (3n² – 10n + 7) = 6n – 7

Reason is correct.

Therefore, Both A and R are true and R is the correct explanation for A.

They form an A.P. with,

a = 10 , d = 10

Reason is correct.

Since √2 and −√2 are the zeroes of 2x⁴−3x³−3x²+6x−2, then(x−√2) (x+√2) are the factors of given polynomial i.e., 
(x−√2) (x+√2) = (x²−2) is a factor of given polynomial. 
∴p(x) = 2x⁴−3x³−3x²+6x−2
⇒ p(x) = (x²−2)(2x²−3x+1)

⇒ p(x) = (x² - 2) [2x² - 2x - x + 1]
⇒ p (x) = (x² - 2) [2x (x -1) - 1 (x - 1)]
⇒ p (x) = (x² - 2) (x -1) (2x -1)
∴ Other zeroes are x - 1 = 0 and 2x - 1 = 0 ⇒ x = 1 and x = 1/2

= ( a² + b² + c² - ab - bc - ca )

By multiplying it by 2 and dividing it by 2.

= 2 ( a² + b² + c² - ab - bc - ca ) ÷ 2

= ( 2a² + 2b² + 2c² - 2ab - 2bc - 2ca ) ÷ 2

= ( a² + a² + b² + b² + c² + c² - 2ab - 2bc - 2ca ) ÷ 2

= ( a² + b² - 2ab + b² + c² - 2bc + a² + c² - 2ca ) ÷ 2

= [ ( a - b )² + ( b - c )² + ( a - c )² ] ÷ 2

Now , whatever is the value of  ( a - b ) , ( b - c ) and ( a - c ) but its square will be always positive, and 2 is also a positive number.

So, the sum of ( a - b )², ( b - c )² and ( a - c )² will be a positive number and if a positive number is divided by a positive number then the result is also a positive number.

So, it is a positive number,hence it can't be a negative number.

The assertion and reason are both true, but the reason does not directly explain k=2 when one zero is the reciprocal of the other. The calculation to find k would involve using the relationship between the product of the roots and the constants in the polynomial, which is not mentioned in the reason.

Internal angles of a regular Hexagon = 120°